[2] (A) f'(a) = √ 1 – f ± (a) for all a ∈ (0, (B) f'(a) = = true (0) 2 -- for all a E (C) f(a) f'(a) for atleast one a E T 8a D) f'(a) = for atleast one a E (0, 2). 2 T माना f : [0, 72 -> [0, 1] एक अवकलनीय फलन इस प्रकार है, कि f(0) = 0, f (A) सभी a ∈ (0, ½) के लिये f'(a) = E 1 – f 2 (a) होगा (0₁). (0, 7) टे (5) = 1 हो, तब =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Let f: [0]
22] → [0, 1] be a differentiable function such that f(0) = 0, f (22) = 1, then
T
(A) f'(a) = 1 – f 2 (a ) for all a E
(0, 27 ).
(B) ra) = 2 for alle e (0. 1).
f'(a)
= a E
T
(C) f(a) f'(a) =
for atleast one a E
(0, 2 )
T
8a
for atleast one a E
(0, 1).
2
ग
->>
[0, 1] एक अवकलनीय फलन इस प्रकार है, कि f(0) = 0, f (27) 1 हो, तब
=
2½
½ ) के लिये f'(a) =
1 – f 2 (a) होगा
(0, 5, 7) के लिये f'(a)
होगा
T
T
के लिये f(a) f '(a) =
होगा
T
8a.
(0, 2½ ½) के लिये f'(a) =
2
(D) f'(a) =
माना f:
2
(A) सभी a. ∈ (0,
(B) सभी a. E
(C) कम से कम एक a E
(D) कम से कम एक a E
=
2-
T
होगा
Transcribed Image Text:Let f: [0] 22] → [0, 1] be a differentiable function such that f(0) = 0, f (22) = 1, then T (A) f'(a) = 1 – f 2 (a ) for all a E (0, 27 ). (B) ra) = 2 for alle e (0. 1). f'(a) = a E T (C) f(a) f'(a) = for atleast one a E (0, 2 ) T 8a for atleast one a E (0, 1). 2 ग ->> [0, 1] एक अवकलनीय फलन इस प्रकार है, कि f(0) = 0, f (27) 1 हो, तब = 2½ ½ ) के लिये f'(a) = 1 – f 2 (a) होगा (0, 5, 7) के लिये f'(a) होगा T T के लिये f(a) f '(a) = होगा T 8a. (0, 2½ ½) के लिये f'(a) = 2 (D) f'(a) = माना f: 2 (A) सभी a. ∈ (0, (B) सभी a. E (C) कम से कम एक a E (D) कम से कम एक a E = 2- T होगा
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